An Example

Two roofing systems are examined. The systems are identical, except for the insulation material.
Both are analyzed for the climate in Chicago with an indoor relative humidity of 50% and indoor
temperature of 68°F. Both have a black outer membrane and a tight metal deck. Fiberboard and
foam systems are analyzed. Insulation thickness is 3 inches for both.

Requirement 1:Both systems pass requirement 1, since the H of Chicago is 6151 which is less
than or equal to 8992.

These results are common for both systems. Then, using Equation (4), for fiberboard:

m

=

0.215 (6.4)(0.171-0.110)/(0.211 +1.56 + 0.071)

m

=

0.046 lb/ft2

The failure threshold for fiberboard is 0.20 lb/ft2. Since 0.046<0.20 lb/ft2, this system passes.
Using Equation (4) again, this time for foam:

m

=

0.215 (6.4)(0.171-0.110)/(0.211 +1.56 + 1.39)

m

=

0.027 lb/ft2

The failure threshold for foam systems is 0.012 lb/ft2. Since 0.027>0.012 lb/ft2, this system fails.

Requirement 3:

For the fiberboard system, the condition for failure is not met, so this system passes.

For the foam system, the vapor resistance ratio is calculated:

Ri/Rd = 1.39/1.56 = 0.9.

Since 0.9 < 1.5, we fail.

Requirement 4:

Using Eqns. 7 and 8 to determine the relative time to dry for the fiberboard and foam
systems:

t = 3 months (for fiberboard)
t = 7 months (for foam)

The fiberboard system dries more quickly than the foam system, but both dry in less than
the maximum of twelve months.

The fiberboard system passes all four requirements and therefore represents an acceptable
design for moisture control for this roofing application. The foam system would likely
see condensation at the roof membrane in the winter and represents a poor design for
moisture control in this case.